Details

sample145.0ms

Algorithm

intervals

Results

70.0ms	50×	body	2560	valid
24.0ms	41×	body	1280	valid
20.0ms	50×	body	640	valid
7.0ms	19×	body	320	valid
7.0ms	75×	body	80	valid
4.0ms	21×	body	160	valid

simplify49.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize14.0ms

Local error

Found 2 expressions with local error:

14.7b	(/ (- 1 (cos x)) (* x x))
1.8b	(- 1 (cos x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cbrt-cube` `add-exp-log`
6×	`times-frac` `associate-/l*` `difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`distribute-lft-out--`
2×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `insert-posit16` `flip--` `associate-/l/`
1×	`clear-num` `associate-/r*` `sub-neg` `frac-2neg` `diff-log` `div-sub` `prod-exp` `cbrt-unprod` `div-inv`

Counts

2 → 47

Calls

2 calls:

Slowest

43.0ms	(/ (- 1 (cos x)) (* x x))
11.0ms	(- 1 (cos x))

series142.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

101.0ms	(/ (- 1 (cos x)) (* x x))
41.0ms	(- 1 (cos x))

simplify809.0ms

Counts: 53 → 53

prune369.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

14.6b	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
0.4b	(+ 1 (cos x))
0.3b	(* (sin x) (sin x))
0.2b	(/ (* (sin x) (sin x)) (+ 1 (cos x)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`*-un-lft-identity`
22×	`times-frac`
16×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r/` `add-log-exp`
5×	`associate-/r*` `distribute-lft-out`
4×	`flip3-+` `flip-+` `insert-posit16` `div-inv`
3×	`div-sub` `swap-sqr` `associate-r` `associate-l` `sqr-sin`
2×	`clear-num` `frac-2neg` `sin-mult` `associate-/l/`
1×	`pow2` `+-commutative` `sum-log` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

Slowest

31.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
24.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
17.0ms	(* (sin x) (sin x))
5.0ms	(+ 1 (cos x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

99.0ms	(/ (/ (* (sin x) (sin x)) (+ 1 (cos x))) (* x x))
65.0ms	(/ (* (sin x) (sin x)) (+ 1 (cos x)))
34.0ms	(* (sin x) (sin x))
11.0ms	(+ 1 (cos x))

simplify642.0ms

Counts: 127 → 127

prune1.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (tan (/ x 2)) x)
0.1b	(/ (sin x) x)
0.1b	(* (/ (sin x) x) (/ (tan (/ x 2)) x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r` `associate-l`
6×	`cbrt-undiv` `associate-/r` `div-exp` `associate-/l`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`frac-times` `pow-prod-down` `associate-l/` `tan-quot` `associate-r/` `*-commutative` `associate-/l/`

Counts

3 → 108

Calls

3 calls:

Slowest

28.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
8.0ms	(/ (sin x) x)
6.0ms	(/ (tan (/ x 2)) x)

series262.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

124.0ms	(* (/ (sin x) x) (/ (tan (/ x 2)) x))
100.0ms	(/ (tan (/ x 2)) x)
38.0ms	(/ (sin x) x)

simplify2.5s

Counts: 117 → 117

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (/ (sin x) x))
0.3b	(cbrt (/ (sin x) x))
0.3b	(cbrt (/ (sin x) x))
0.3b	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 148

Calls

4 calls:

Slowest

15.0ms	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))
2.0ms	(cbrt (/ (sin x) x))
1.0ms	(cbrt (/ (sin x) x))
1.0ms	(cbrt (/ (sin x) x))

series787.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

226.0ms	(cbrt (/ (sin x) x))
194.0ms	(* (cbrt (/ (sin x) x)) (cbrt (/ (sin x) x)))
191.0ms	(cbrt (/ (sin x) x))
176.0ms	(cbrt (/ (sin x) x))

simplify1.8s

Counts: 160 → 160

prune1.8s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes55.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch2.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.7s	1641×	body	2560	valid
1.4s	1245×	body	1280	valid
826.0ms	1486×	body	640	valid
362.0ms	904×	body	320	valid
356.0ms	2247×	body	80	valid
106.0ms	477×	body	160	valid